Timing and probability of arrival for sea lice dispersing between salmon farms

Sea lice are a threat to the health of both wild and farmed salmon and an economic burden for salmon farms. With a free-living larval stage, sea lice can disperse tens of kilometres in the ocean between salmon farms, leading to connected sea louse populations that are difficult to control in isolation. In this paper, we develop a simple analytical model for the dispersal of sea lice (Lepeophtheirus salmonis) between two salmon farms. From the model, we calculate the arrival time distribution of sea lice dispersing between farms, as well as the level of cross-infection of sea lice. We also use numerical flows from a hydrodynamic model, coupled with a particle tracking model, to directly calculate the arrival time of sea lice dispersing between two farms in the Broughton Archipelago, British Columbia, in order to fit our analytical model and find realistic parameter estimates. Using the parametrized analytical model, we show that there is often an intermediate interfarm spacing that maximizes the level of cross-infection between farms, and that increased temperatures will lead to increased levels of cross-infection.